victoria invested $9,300 in an account paying an interest rate of 4.5% …
$12743.60$
Question
victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?
Solution Steps
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Understand the question
victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?
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Explanation
Step1: Recall continuous compound formula
The formula for continuous compounding is $A = Pe^{rt}$, where:
- $P$ = principal amount,
- $r$ = annual interest rate,
- $t$ = time in years,
- $A$ = final amount.
Step2: Identify given values
$P = 9300$, $r = 0.045$, $t = 7$
Step3: Substitute values into formula
$A = 9300 \times e^{(0.045 \times 7)}$
Step4: Calculate exponent term
First compute $0.045 \times 7 = 0.315$, so $A = 9300 \times e^{0.315}$
Step5: Compute final amount
$e^{0.315} \approx 1.37028$, then $A \approx 9300 \times 1.37028 = 12743.604$
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Final answer
$12743.60$
Answer
Explanation
Step1: Recall continuous compound formula
The formula for continuous compounding is $A = Pe^{rt}$, where:
- $P$ = principal amount,
- $r$ = annual interest rate,
- $t$ = time in years,
- $A$ = final amount.
Step2: Identify given values
$P = 9300$, $r = 0.045$, $t = 7$
Step3: Substitute values into formula
$A = 9300 \times e^{(0.045 \times 7)}$
Step4: Calculate exponent term
First compute $0.045 \times 7 = 0.315$, so $A = 9300 \times e^{0.315}$
Step5: Compute final amount
$e^{0.315} \approx 1.37028$, then $A \approx 9300 \times 1.37028 = 12743.604$
Answer
$12743.60$
Question Image
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Subject
mathematics
Sub Subject
calculus
Education Level
high school
Difficulty
unspecified
Question Type
calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:08:50
OCR Text
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victoria invested $9,300 in an account paying an interest rate of 4.5% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 7 years?
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